1mathieu0.mac and mathieu.mac are from the book "Computer Algebra in
2Applied Mathematics: An introduction to MACSYMA", by Richard H Rand,
3Pitman (1984).
4
5Mathieu's equation is x''+(delta+e*cos(t))*x=0
6
7For given values of the parameters delta and e, either all the
8solutions are bounded (the equation is stable) or there exist
9unbounded solutions (the equation is unstable).  The regions of
10stability are separated from thos of instability by "transition
11curves".
12
13This program computes the transition curves for n=0 (mathieu0.mac) and
14n>0 (mathieu.mac) in Mathieu's equation using a perturbation method.
15
16The run below, using maxima-5.9.0cvs, reproduces the result on pages
1790-94 of the book.
18
19(C1) load("./mathieu0.mac");
20(D1)                            ./mathieu0.mac
21(C2) mathieu0();
22ENTER DEGREE OF TRUNCATION
238;
24              8       6      4    2
25       68687 e    29 e    7 e    e
26delta= -------- - ----- + ---- - --
27        294912     144     32    2
28
29
30(C1) load("./mathieu.mac");
31(D1)                             ./mathieu.mac
32(C2) mathieu();
33ENTER TRANSITION CURVE NUMBER N
341;
35ENTER DEGREE OF TRUNCATION
366;
37           6       5    4     3    2
38       49 e    11 e    e     e    e    e   1
39delta= ----- - ----- - --- + -- - -- - - + -
40       36864   4608    384   32   8    2   4
41
42           6       5    4     3    2
43       49 e    11 e    e     e    e    e   1
44delta= ----- + ----- - --- - -- - -- + - + -
45       36864   4608    384   32   8    2   4
46
47(D2)
48(C3) mathieu();
49ENTER TRANSITION CURVE NUMBER N
502;
51ENTER DEGREE OF TRUNCATION
526;
53                6        4      2
54       1002401 e    763 e    5 e
55delta= ---------- - ------ + ---- + 1
56        4976640      3456     12
57
58              6       4    2
59         289 e     5 e    e
60delta= - ------- + ---- - -- + 1
61         4976640   3456   12
62
63
64Local Variables: ***
65mode: Text ***
66End: ***